Jan ŠLAMBERGER1, Mario VRAŽIĆ2, Peter VIRTIČ1,
University of Maribor, Faculty of Energy Technology (1), University of Zagreb, Faculty of Electrical Engineering and Computing (2)
Comparison of single- and double-layer windings in an axial flux
permanent-magnet synchronous machine
Abstract. This paper deals with the comparison between single-layer and double-layer concentrated windings in an axial flux permanent magnet
synchronous machine. The results are obtained using finite element method and present the differences in back electromotive force, cogging torque,
detent force and static torque for both winding topologies.
Streszczenie. W artykule przedstawiono porównanie między pojedyńczo- i podwójnie-warstwowymi uzwojeniami koncentrycznymi maszynach
synchronicznych z magnesami trwałymi i strumieniem osiowym. Do tego porównania wykorzystano metodę elementów skończonych, a wyniki
analizy prezentują różnice we wstecznej sile elektromotorycznej, momentach pulsacyjnych, sile zaczepu i momencie statycznym dla obu topologii
uzwojenia. (Porównanie pojedynczo- i podwójnie-warstwowych uzwojeń w maszynie synchronicznej z magnesami trwałymi i strumieniem
osiowym)
Keywords: axial flux, permanent magnet, synchronous machine, winding.
Słowa kluczowe: strumień osiowy, magnes trwały, maszyna synchroniczna, uzwojenie.
doi:10.12915/pe.2014.12.41
Introduction
The concentrated windings in an axial flux permanent
magnet synchronous machine (AFPMSM) may be wounded
as single- or double-layer windings. In case of a single-layer
winding only every second tooth is wounded, meanwhile in
case of a double-layer winding every tooth is wounded (Fig.
1) [1]. The comparison of characteristics of AFPMSMs with
single-layer and double-layer concentrated windings will be
a focus of this paper. The proposed calculation method is
based on finite element method (FEM), which can be used
for diagnostics of the damage rotor elements of induction
motor [2-3], inter-coil short circuit detection [4],
unsymmetrical load calculation [5], and in automated
detection of the anomalies [6-7]. AFPMSM can be used
also for the wind energy exploitation in Slovenia [8-9].
The AFPMSMs used in this paper have the same shape
and amount of cooper and rotor iron cores. The cogging
torque, the back electromotive force, the detent force and
the static torque are calculated with FEM using software
package ANSYS workbench V14.0. The procedure of
numerical calculations was verified with analytical methods
and measurements in [10] and [11].
- Stator cores
- Upper layer windings
- Rotor cores
- Windings
- Lower layer windings
- PMs
Fig.1. Topologies of AFPMSMs
Maxwell’s equation for magnetic field calculation
For the magnetic field calculation the system of
equations (1)-(3) for the magnetostatic problem has to be
solved.
(1)
(2)
 H  J
B  0
B   r 0 H  0 M
(3)
where: H – magnetic field intensity, J – current density to
due to movement of free charges, B – magnetic flux
density, μ0 – the permeability of free space and μr – relative
permeability of the associated region.
168
Magnetic flux density can be represented with magnetic
vector potential as in (4).
(4)
B   A
Calculation of Back Electromotive Force
Back electromotive force (EMF) of the AFPMSM at noload is calculated using Faraday’s law of electromagnetic
induction based on the time variation of magnetic flux (5).
The magnetic flux can be obtained through the magnetic
flux density on the cross-section surface inside the coil
which has to be perpendicular to the magnetic flux path (6).
(5)
(6)

t
   BdS
e  N
S
where: e – EMF, N – number of turns,  t – time
variation of magnetic flux within the coil, S – surface.
Torque and force calculation
Forces are calculated using Maxwell’s stress tensor
method as in (7), (8) and (9).
(7)
1

1
2
Fx    Bx  B  n  
B nx dS
2


S 
(8)
1

1
2
Fy    B y  B  n  
B n y dS
2


S 
(9)
1

1
2
Fz    Bz  B  n  
B nz dS
2


S 
where: n - normal to the surface.
Torque is calculated as a vector product of radius r and
force F as in (10).
(10)
T rF
Torque around z-axis is calculated as in (11).
(11)
Tz  rx Fy  ry Fx
where: rx – distance in x-axis, ry – distance in y-axis.
PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 12/2014
Topologies of analysed AFPMSMs
Two topologies of the stator and the rotor of AFMPSMs
are apart from the difference of stator windings completely
the same. Even more, also the volume of cooper used for
windings is the same in both cases. The detailed
parameters of AFPMSMs are presented in Table 1.
Table 1. Parameters of AFPMSMs
Single-layer
Double-layer
AFPMSM
AFPMSM
Item
Value [unit]
Value [unit]
Number of coils
6
12
Number of turns
100
50
2
Wire diameter
1,23 [mm ]
Current
10 [A]
Coil area width
20 [mm]
Coil area height
15 [mm]
7,5 [mm]
Coil pitch
30 [deg]
Mechanical air-gap
1 [mm]
Disk radius
150 [mm]
Height of PMs
10 [mm]
Width of PMs
5 [mm]
Length of PMs
60[mm]
Number of poles
10
Number of rotor
2
discs
Remanence of PMs
1,22 [T]
Stator
3
4
5
6
7
8
9
10
11
0
-1/2
Fig.5. Distibution of current density in the coil sides along the
periphery of AFPMSM with double-layer windings at the moment
which corresponds to t=0
Figure 6 shows the star of slots, where E1, E2, E3…E12
are back EMFs phasors of the slots and α is electrical angle
between two adjacent slots. Figure 7 shows the sum of
connected sides of coils and the phase back EMFs. The
sum of connected sides of coils is calculated on basis of
connections presented in Fig. 2 and Fig. 4. The phase back
EMFs are calculated for single-layer windings by using
equations (12)-(14) and for double-layer windings with (15)(17).
Rotor
2
1
1/2
-1
(12)
To achieve a 10-pole machine, coils have to be
connected in the way, which is presented for the singlelayer windings presented in Fig. 2 and for the double-layer
windings (Fig. 4). The number of poles is verified with a
diagram of current density distribution in coil sides along the
periphery of AFPMSM. Fig. 3 and 5 show a distribution of
current density at the moment which corresponds to the
time t=0.
1
J
(13)
(14)
 
 
U   E1  E2   cos     E7  E8   cos  
2
2
 
 
V   E5  E6   cos     E11  E12   cos  
2
2
 
 
W   E9  E10   cos     E3  E4   cos  
2
2
E
E
E2
E
 cos   12  cos   E7  6  cos   8  cos 
2
2
2
2
E6
E10
E4
E12
(16) V  E5   cos    cos   E11 
 cos  
 cos 
2
2
2
2
E
E
E
E
(17) W  E3  2  cos   4  cos   E9  8  cos   10  cos 
2
2
2
2
(15) U  E1 
12
E9 -E10
-E8
U1
W2
V1
U2
W1
E1
-E6
Fig.2. Connections between coils of single-layer stator windings
-E12
E7
V2
E5
J
1
E11
-E4
E3
-E2
1/2
Fig.6. Star of slots
0
-1/2
-1
Fig.3. Distribution of current density in coil sides along the
periphery of AFPMSM with single-layer stator windings at the
moment which corresponds to t=0
1
U1
2
3
W2
4
5
6
V1
7
U2
8
9
10 11 12
W1
V2
Fig.4. Connections between coils of double-layer stator windings
PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 12/2014
169
THD: 5.5036%
1
0.8
Amplitude
0.6
0.4
0.2
0
0
5
10
Harmonic
15
20
Fig.11. Back EMF harmonic components of double-layer AFPMSM
Cogging torque [Nm]
1
Fig.7. Vector sum of slots EMFs per phase for a) single-layer
winding and b) double-layer winding (U, V and W are phase back
EMFs)
0
5
10
15
20
25
Rotational angle [degree]
30
35
Fig.12. Cogging torque of single-layer AFPMSM
1
100
Back EMF [V]
-0.5
-1
Single-layer AFPMSM
150
0
Cogging torque [Nm]
Calculated results
Figures 8-17 show the results of calculations for
AFPMSM with single-layer winding and with double-layer
winding. The back electromotive force (back EMF) and the
cogging torque were calculated at no-load and speed 1500
rpm. The detent force and the static torque were calculated
at the load of 10 A, where the current density is 8.13
A/mm2.
0.5
50
0.5
0
-0.5
0
-1
-50
0
5
-100
10
15
20
25
Rotational angle [degree]
30
35
Fig.13. Cogging torque of double-layer AFPMSM
-150
0
10
20
30
40
50
Rotational angle [degree]
60
6000
70
5000
Fig.8. Back EMF of single-layer AFPMSM
Detent Force [N]
Double-layer AFPMSM
150
Back EMF [V]
100
50
0
3000
2000
1000
-50
0
0
-100
-150
0
10
20
30
40
50
Rotational angle [degree]
60
70
10
20
30
40
50
Rotational angle [degree]
60
70
60
70
Fig.14. Detent force of single-layer AFPMSM
Fig.9. Back EMF of double-layer AFPMSM
6000
THD: 9.9332%
1
5000
0.8
4000
Detent Force [N]
Amplitude
4000
0.6
0.4
3000
2000
1000
0.2
0
0
0
0
5
10
Harmonic
15
20
Fig.10. Back EMF harmonic components of single-layer AFPMSM
170
10
20
30
40
50
Rotational angle [degree]
Fig.15. Detent force of double-layer AFPMSM
PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 12/2014
40
REFERENCES
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Static torque [Nm]
20
10
0
-10
-20
-30
-40
0
10
20
30
40
50
Rotational angle [degree]
60
70
Fig.16. Static torque of single-layer AFPMSM
40
30
Static torque [Nm]
20
10
0
-10
-20
-30
-40
0
10
20
30
40
50
Rotational angle [degree]
60
70
Fig.17. Static torque of double-layer AFPMSM
Conclusion
The comparison between calculated results of
AFPMSMs with single- and double-layer windings shows
that there is only a small difference in characteristics
between these two machines. The main difference is in the
shape and the peak value of back EMFs. The reason for
that are the winding factors, which are a little bit smaller in
case of double-layer windings and total harmonic distortion
(THD), which is for 80% greater in case of single-layer
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picture about the performance abilities of the two types of
windings.
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Authors: assist. Jan Šlamberger B. Sc. E. E., University of
Maribor, Faculty of Energy Technology, Hočevarjev trg 1, 8270
Krško, Slovenia, E-mail: jan.slamberger@uni-mb.si; assoc. prof.
Mario Vražić, Ph.D., University of Zagreb, Faculty of electrical
engineering and computing, Unska 3, 10000 Zagreb, Croatia, Email: mario.vrazic@fer.hr; assoc. prof. Peter Virtič, Ph.D.,
University of Maribor, Faculty of Energy Technology, Hočevarjev
trg 1, 8270 Krško, Slovenia, E-mail: peter.virtic@uni-mb.si.
PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 12/2014
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